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Physics 2211001, Fall 2008
basic kinematics
Due at 11:00pm on Sunday, August 24, 2008
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Given Positions, Find Velocity and Acceleration
Learning Goal:
To understand how to graph position, velocity, and acceleration of an object starting with a table
of positions vs. time.
The table shows the
x
coordinate of a moving object. The position is tabulated at 1s intervals. The
x
coordinate is
indicated below each time. You should make the simplification that the acceleration of the object is bounded and
contains no spikes.
time (s)
0
1
2
3
4
5
6
7
8
9
x
(m)
0
1
4
9
16
24
32
40
46
48
Part A
Which graph best represents the function
, describing the object's position vs. time?
Hint A.1
Meaning of a bounded and nonspiky acceleration
Hint not displayed
ANSWER:
1
2
3
4
Part B
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Which of the following graphs best represents the function
, describing the object's velocity as a function of
time?
Part B.1
Find the velocity toward the end of the motion
Part not displayed
Part B.2 What are the implications of zero velocity?
Part not displayed
Part B.3
Specify the characteristics of the velocity function
Part not displayed
ANSWER:
1
2
3
4
In principle, you could also just compute and plot the average velocity. The expression for the average velocity
is
.
The notation
emphasizes that this is not an instantaneous velocity, but rather an average over an
interval. After you compute this, you must put a single point on the graph of velocity vs. time. The most
accurate place to plot the average velocity is at the middle of the time interval over which the average was
computed.
Also, you could work back and find the position from the velocity graph. The position of an object is the
integral of its velocity. That is, the area under the graph of velocity vs. time from
up to time
must equal
the position of the object at time
. Check that the correct velocity vs. time graph gives you the correct position
according to this method.
Part C
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Which of the following graphs best represents the function
, describing the acceleration of this object?
Part C.1
Find the acceleration toward the end of the motion
Part not displayed
Part C.2 Calculate the acceleration in the region of constant velocity
Part not displayed
Part C.3
Find the initial acceleration
Part not displayed
ANSWER:
1
2
3
4
In one dimension, a linear increase or decrease in the velocity of an object over a given time interval implies
constant acceleration over that particular time interval. You can find the magnitude of the acceleration using the
formula for average acceleration over a time interval:
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 Fall '08
 DUNCAN
 Physics

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